Find the value of

(i)     ${\text{A}}$;

(ii)     ${\text{B}}$;

(iii)     ${\text{C}}$.

Calculate the probability that Tomek wears

(i)     shorts and no tie;

(ii)     no tie;

(iii)     shorts given that he is not wearing a tie.

The conference lasts for two days.

Calculate the probability that Tomek wears trousers on both days.

The conference lasts for two days.

Calculate the probability that Tomek wears trousers on one of the days, and shorts on the other day.

(i)     $0.7 \left( {\frac{{70}}{{100}},{\text{ }}\frac{7}{{10}},{\text{ 70% }}} \right)$     (A1)

(ii)     $0.2 \left( {\frac{{20}}{{100}},{\text{ }}\frac{2}{{10}},{\text{ }}\frac{1}{5},{\text{ 20% }}} \right)$     (A1)

(iii)     $0.85 \left( {\frac{{85}}{{100}},{\text{ }}\frac{{17}}{{20}},{\text{ 85% }}} \right)$     (A1)

[3 marks]

(i)     $0.7 \times 0.85$     (M1)

Note: Award (M1) for multiplying their values from parts (a)(i) and (a)(iii).

$= 0.595{\text{ }}\left( {\frac{{119}}{{200}},{\text{ 59.5% }}} \right)$     (A1)(ft)(G1)

Note: Follow through from part (a).

(ii)     $0.3 \times 0.2 + 0.7 \times 0.85$     (M1)(M1)

Note: Award (M1) for their two products, (M1) for adding their two products.

$= 0.655{\text{ }}\left( {\frac{{131}}{{200}},{\text{ 65.5% }}} \right)$     (A1)(ft)(G2)

Note: Follow through from part (a).

(iii)     $\frac{{0.595}}{{0.655}}$     (A1)(ft)(A1)(ft)

Notes: Award (A1)(ft) for correct numerator, (A1)(ft) for correct denominator. Follow through from parts (b)(i) and (ii).

$= 0.908{\text{ }}\left( {{\text{0.90839}} \ldots ,{\text{ }}\frac{{119}}{{131}},{\text{ 90,8% }}} \right)$     (A1)(ft)(G2)

[8 marks]

$0.3 \times 0.3$     (M1)

$= 0.09 \left( {\frac{9}{{100}}, 9\%} \right)$     (A1)(G2)

[2 marks]

$0.3 \times 0.7$     (M1)

$0.3 \times 0.7 \times 2$   OR   $(0.3 \times 0.7) + (0.7 \times 0.3)$     (M1)

Note: Award (M1) for their correct product seen, (M1) for multiplying their product by 2 or for adding their products twice.

$= 0.42 \left( {\frac{{42}}{{100}}, \frac{{21}}{{50}}, 42\%} \right)$     (A1)(ft)(G2)

Note: Follow through from part (a)(i).

[3 marks]